Chapter 17.7, Problem 19E

Stokes’ Theorem for evaluating surface integrals Evaluate the line integral in Stakes’ Theorem to determine the value of the surface integral ${\displaystyle {\iint }_S\left(\nabla \times F\right)\cdot ndS}$. Assume that n points in an upward direction.

19.    F = 〈2y – z, x – y – z〉; S is the cap of the sphere (excluding its base) x² + y² + z² = 25, for 3 ≤ x ≤ 5.